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<p>In this paper we study logarithmic double phase problems with superlinear right-hand sides and nonlinear Neumann boundary condition. In particular, we show that the problem under consideration has a least energy sign-changing solution. The proof is based on the minimization of the energy functional over the related nodal Nehari manifold along with the Poincaré–Miranda existence theorem. As a result of independent interest, we prove the existence of a new and very general equivalent norm in the logarithmic Musielak–Orlicz Sobolev space. In addition, we present a priori bounds for a large class of logarithmic double phase problems involving convection terms for critical and subcritical situations.</p>

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Least energy sign-changing solution for logarithmic double phase problems with nonlinear boundary condition

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月16日

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  • Franziska Borer,
  • Leszek Gasiński,
  • Matheus F. Stapenhorst,
  • Patrick Winkert

摘要

In this paper we study logarithmic double phase problems with superlinear right-hand sides and nonlinear Neumann boundary condition. In particular, we show that the problem under consideration has a least energy sign-changing solution. The proof is based on the minimization of the energy functional over the related nodal Nehari manifold along with the Poincaré–Miranda existence theorem. As a result of independent interest, we prove the existence of a new and very general equivalent norm in the logarithmic Musielak–Orlicz Sobolev space. In addition, we present a priori bounds for a large class of logarithmic double phase problems involving convection terms for critical and subcritical situations.